The following examples illustrate the Gauss elimination procedure.

- Interchange
and
equation (or
).
- Divide the
equation by
(or
).
- Add
times the
equation to the
equation
(or
).
- Add
times the
equation to the
equation (or
).
- Multiply the
equation by
(or
).

The last equation gives the second equation now gives Finally the first equation gives Hence the set of solutions is A UNIQUE SOLUTION.

- Add
times the first equation to the second equation.
- Add
times the first equation to the third equation.
- Add
times the second equation to the third equation

- Add
times the first equation to the second equation.
- Add
times the first equation to the third equation.
- Add
times the second equation to the third equation

This can never hold for any value of Hence, the system has NO SOLUTION.

A K Lal 2007-09-12